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License plates are not truly random, there is a logical system that each state uses. People living within the same area as you may have very similar tags, because that same three letter pattern could have been granted to thousands of your neighbors depending on when they went to the DMV.

So to answer your question, the odds are much higher on your daily commute than, say, driving cross-country, in which case it would be considerably low considering all of the variables involved.

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Q: What are the odds of seeing the same three letters in the same order on a license plate over and over in a month?
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